Symposium in honor of Rodney J. Clifton Symi, Greece, 24-29 June 2012 Materials Physics of Faults in Rapid Shear and Consequences for Earthquake Dynamics James R. Rice (Harvard) Underlying studies done collaboratively with some of: Nicolas Brantut (Univ Col Lond) Massimo Cocco (INGV Rome) Eric Dunham (Stanford) Nadia Lapusta (Caltech) Hiroyuki Noda (JAMSTEC) John Platt (Harvard) Alan Rempel (Oregon) John Rudnicki (Northwestern) Victor C. Tsai (Caltech)
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Symposium in honor of Rodney J. CliftonSymi, Greece, 24-29 June 2012
Materials Physics of Faults in Rapid Shearand Consequences for Earthquake Dynamics
James R. Rice (Harvard)
Underlying studies done collaboratively with some of:
Nicolas Brantut (Univ Col Lond) Massimo Cocco (INGV Rome) Eric Dunham (Stanford) Nadia Lapusta (Caltech) Hiroyuki Noda (JAMSTEC) John Platt (Harvard) Alan Rempel (Oregon) John Rudnicki (Northwestern) Victor C. Tsai (Caltech)
Rod Clifton's influence on, and direct contributions to, mechanics in earth science and engineering:
Pioneer of the mechanics of hydraulic fracture • Fracture mechanics of crack development from pressurizedboreholes. • Hydrofracture measurements to infer in-situ principal stresses. • Vertical containment of fractures. • Efficient numerical procedures to address the coupled fluid-solidmechanics in 3D.
Dynamics of shear localization in thermally-softening ductile solids
Frictional sliding at high rates - oblique plate impact • Friction is low at high rates. • Abrupt change in normal stress σ does not cause abrupt change inshear stress τ -- critical to well-posed bimaterial fault sliding models!
[Rice, JGR 2006]
Punchbowl PSS, composite based on Chester & Chester [Tectonophys ‘98] & Chester & Goldsby [SCEC ‘03]
5 mm
Earthquake shear is highly localized!
[Heermance, Shipton & Evans, BSSA, 2003]Core retrieved across the Chelungpu fault, which hosted the 1999 Mw 7.6 Chi-Chi,Taiwan, earthquake: Suggests slip at 328 m depth traversewas accommodated within a zone ~ 50–300 μm thick.
• Hole B, fault at 1136 m depth: PSZ is ~3 mm thickPSZ layering defined by variations in concentrations of clay minerals and clasts,comparable to structures produced in high-rate rotary shear experiments.
Two other Chelungpu Fault,Taiwan boreholes[Boullier et al., GGG 2009, GSL 2011]:Principal Slip Zone (PSZ) localized within black gouges
• Hole A, fault at 1111 m depth: PSZ is ~2 cm thick
A
B
h ≈ 3 mmWibberley (2003)
Median TectonicLine Fault, Japan
k,
q = −k
η f(∇p − ρ f g)
= fluid flux relative to solid host
Quandary in seismology:
• Lab estimates of friction coefficient are usually high, f ~ 0.6-0.8.
Shear strength τ = f x (σn – p), where:
σn = normal stress clamping the fault shut p = pore pressure in infiltrating fluid phase
• Fault slip zones are thin (despite wide damage zones, 1-103 m).
==> If those f prevail during seismic slip, we should find
• measurable heat outflow near major faults, and/or
• extensive melting along exhumed faults.
Neither effect is generally found.
One line of explanation: Weak faults: τ = f x (σn – p)
• Fault core materials are different, have very low f (e.g., like some clays).
• f isn’t low, but pore pressure p is high over much of the fault.
Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:
• Processes expected to be important from start of seismic slip:
- Flash heating of asperity contacts, reduces f in rapid slip.
- Thermal pressurization of in-situ pore fluid, reduces effective stress.
• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure
(e.g., CO2 from carbonates; H2O from clays or serpentines).
- Gel formation at large slip in wet silica-rich faults.
- Nanoparticle weakening, physics still unclear.
• Ultimately:
- Melting at large slip, if above set has not limited increase of T.
One line of explanation: Weak faults: τ = f x (σn – p)
• Fault core materials are different, have very low f.
• f isn’t low, but pore pressure p is high over much of the fault.
Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:
• Processes expected to be important from start of seismic slip:
- Flash heating of asperity contacts, reduces f in rapid slip.
- Thermal pressurization of in-situ pore fluid, reduces effective stress.
• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure
(e.g., CO2 from carbonates; H2O from clays or serpentines).
- Gel formation at large slip in wet silica-rich faults.
- Nanoparticle weakening, physics still unclear.
• Ultimately:
- Melting at large slip, if above set has not limited increase of T.
V = slip rate
asperity diameter
T = asperity temperature
Tf = average temperature of fault surfaces
Flash heating of microscopic frictional asperity contacts[Rice, EOS 1999; JGR 2006; Beeler and Tullis, EOS 2003, Beeler et al. JGR 2008,
building on Bowden and Thomas, 1954; Archard, 1958/59; Ettles,1986; Lim and Ashby, 1987.]
contact shear stress
T, asperity temperature
Tf Tw , weakening temperature
τc
"Weakening" slip rate:
Vw = π αthD
Tw − Tfτc ρc
⎛⎝⎜
⎞⎠⎟
2
When V > Vw , asperity
is weak for some of its
life; suggests friction coef
f ≈ fslowVwV
+ fweak 1−VwV
⎛⎝⎜
⎞⎠⎟
= fweak + ( fslow − fweak )VwV
when V > Vw .
~ 0.1 μ
Arkansas novaculite (~100% quartzite)
0.36 m/s
Vw ≈ 0.14 m/s
[Tullis & Goldsby, SCEC, 2003; EOS, 2003]
Rotary shear, 1.2 mm pre-slip at ~10 μm/s, followed by rapid
(Experiment becomesuninterpretable after smallslip, marked, due to crackingin wall of specimen.)
One line of explanation: Weak faults: τ = f x (σn – p)
• Fault core materials are different, have very low f.
• f isn’t low, but pore pressure p is high over much of the fault.
Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:
• Processes expected to be important from start of seismic slip:
- Flash heating of asperity contacts, reduces f in rapid slip.
- Thermal pressurization of in-situ pore fluid, reduces effective stress.
• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure
(e.g., CO2 from carbonates; H2O from clays or serpentines).
- Gel formation at large slip in wet silica-rich faults.
- Nanoparticle weakening, physics still unclear.
• Ultimately:
- Melting at large slip, if above set has not limited increase of T.
Shear of a fluid-saturated gouge layer
• Two undeforming half-spaces are moved relative toeach other at a speed V.
• All deformation accommodated in gouge layer, leadinga to a nominal strain rate,
γ 0 =
V
h .
Thermo-mechanical model in gouge layer
∂p∂t
−αhy
∂2 p∂y2
= Λ ∂T∂t
τ = f (γ )(σ n − p)
∂T∂t
−α th
∂2T∂y2
= τγρc
Mechanical equilibrium
• Shear stress modeled using the effective stress andrate-strengthening friction,
Conservation of fluid mass
Conservation of energy
• To model the deforming gouge layer we use,
f (γ ) = f0 + (a − b)logγγ 0
⎛⎝⎜
⎞⎠⎟
(we assume a − b ≡ γ df (γ ) / dγ( )γ =γ 0> 0)
∂τ∂y
= 0, ∂σn∂y
= 0
Rice, Rudnicki & Platt (in prep for JGR 2012)
V / 2
V / 2
h
Shear between moving rigid blocks of perfectly insulating, impermeable material :
Exact homogeneous shear solution (Lachenbruch,
JGR, 1980,version ignoring dilatancy) :
τ (t) = f σn − p(t)( ) = f σn − p(0)( )exp −foΛρc
γ ot⎛⎝⎜
⎞⎠⎟
, γ o =V
h
[characteristic weakening strain =ρcfoΛ
≈ 10-20, for fo ≈ 0.4]
But is that solution stable?
Not unless h is very small ! (Rice & Rudnicki, AGU, 2005) :
Thickest possible h (call it Wcrit ) for stable
homogeneous shear is Wcrit = λshr / 2,
[λshr = longest wavelenth λ for stable linearized response
to infinitesimal exp(2πiy / λ) perturbation], implying
Wcrit =π 2
2 + foa − b
⎛⎝⎜
⎞⎠⎟
ρcfoΛ
αth +αhy( )V
.
u(y,t) = γ oy =
V
hy
σnτ (t)
Stable only if h ≤Wcrit .
Rice, Rudnicki & Platt (in prep for JGR 2012)
Estimates of maximum stable shear layer thickness Wcrit :
Wcrit =π 2
2 + foa − b
⎛⎝⎜
⎞⎠⎟
ρcfoΛ
αth +αhy( )V
(indep. of σn )
Results, using fo = 0.4, fo
a − b= 20, V = 1
m
s, αth = 0.7
mm2
s, ρc = 2.7
MPa
ºC :
Low estimate (Based on lab properties of intact Median Tectonic Line gouge [Wibberley and Shimamoto,
2003] at effective confining stress = 125 MPa and T = 200ºC -- corresponding to ~ 7 km depth):
Λ = 0.70 MPa
ºC , and αhy = 1.5
mm2
s ⇒ Wcrit = 10 μm
High estimate (Accounts very roughly for fresh damage of the initially intact fault gouge, introduced at the
rupture front just before and during shear, by increasing permeability k to kdmg = 5-10 k, and increasing
drained compressibility βd to βddmg = 1.5-2 βd ):
Λ ≈ 0.34 MPa
ºC , and αhy ≈ 3.5
mm2
s ⇒ Wcrit ≈ 40 μm
Rice, Rudnicki & Platt (in prep for JGR 2012)
(Kitajima, Chester, Chester & Shimamoto, JGR 2010): Rapid rotary shear of thePunchbowl fault gouge: Disaggregated to form Unit 1. Early shear forms Unit 2.Unit 3 (fluffier) formed by T-induced fluid phase change (thermal pressurization). Unit 4 is a localized shear structure.
One line of explanation: Weak faults: τ = f x (σn – p)
• Fault core materials are different, have very low f.
• f isn’t low, but pore pressure p is high over much of the fault.
Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:
• Processes expected to be important from start of seismic slip:
- Flash heating of asperity contacts, reduces f in rapid slip.
- Thermal pressurization of in-situ pore fluid, reduces effective stress.
• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure
(e.g., CO2 from carbonates; H2O from clays or serpentines).
- Gel formation at large slip in wet silica-rich faults.
- Nanoparticle weakening, physics still unclear.
• Ultimately:
- Melting at large slip, if above set has not limited increase of T.
Model for decomposing gouge material
∂p∂t
= Λ ∂T∂t
+αhy
∂2 p∂y2
+ Pr∂ξ∂t
∂T∂t
= τγρc
+α th
∂2T∂y2
− Er
∂ξ∂t
• We assume that the reaction follows an Arrheniuskinetic law,
• To model the deforming gouge layer we use,
∂ξ∂t
= A 1− ξ( )exp − Q
RT⎛⎝⎜
⎞⎠⎟
Platt, Brantut & Rice (AGU, Fall 2011)
Linear stability analysis(linear perturbation from homogenously sheared state)• We track the critical half-wavelength as a function ofthe ambient fault temperature,
λc = 2π αth +αhy( ) (a − b)ρc
f02Λγ 0
λc = 2π αhyErPr
(a − b)ρcf02γ 0
ºCPlatt, Brantut & Rice (AGU, Fall 2011)
Like R&Rthermal press.result.
Different materials• Using the linear stability analysis, we now try to finda prediction for localized zone width by setting,
100
800
500
550
900
Tc (°C)
2163589Gypsum
32586496Talc
8615993627Kaolinite
61252228Lizardite
1864213093Calcite
W (μm)Pr (MPa)Er (K)Mineral
Table from N. Brantut (Platt, Brantut & Rice, AGU, Fall 2011)
Some Consequences for Earthquake Dynamics
Possibly resolving a quandary in seismology:
Major faults operate under low overall drivingstress, in a manner that generates negligibleheat outflow and involves slip on extremelythin zones.
What thermo-hydro-mechanical processesmight cause that?
coworkers:Eric M. Dunham (Stanford Univ.)
Nadia Lapusta (Caltech)Hiroyuki Noda (Caltech)
Alan W. Rempel (Univ. Oregon)
Dynamic rupture simulations, incorporatingflash heating of asperity contacts and thermalpressurization of pore fluid, with parametersconstrained (to the extent possible) bylaboratory observations
[Noda, Dunham & Rice, JGR 2009]
τ bRupture nucleated (bylocal overstressing) onfault under uniformbackground shear stress
Comparing a growing slip pulse at τb = 0.230 (σ0 – p0)to an enlarging shear crack at τb = 0.238 (σ0 – p0)
[Hickman & Zoback, GRL 2004]
Simulations show growing pulse for ~ 0.22-0.24
Partial Summary:
The simulations are based on laboratory friction andporomechanical studies, on geological characterizations of faultzones, and on mathematical modeling of heating andweakening and of elastodynamics.
They have no input from seismology, heat flow, or regionalstress magnitude/direction studies!
Yet they predict results, in particular: • fault operation at low overall shear stress, • self-healing rupture mode, • plausible magnitude range of static stress drop, • scaling of slip with rupture extent, and • scaling of slipping pulse length with rupture extent*,which look somewhat like earthquakes on major faults asconstrained by seismology, heat flow and stress studies.
* May be too small? And what sets scale (nucleation?) not yet clear.
Implications for seismic hazardThe fact that a segment is creeping does notpreclude it from having large coseismic slip.
Page adapted from H. Noda and N. Lapusta (2012)
[Tanikawa and Shimamoto, 2009]
Summary of lab-measured physical propertiesfor the fault that hosted Chi-Chi earthquake